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In a book I'm reading, the author mentioned the launch of Soyuz spacecraft as follows:

What made it more spectacular was how close we were when it lifted off the launch pad. Yuri, Tim and I were sitting on the roof of the search-​and-​rescue tower, about 1.5 km away from the rocket. It was gone 3 a.m. on a beautifully clear night and, when I saw the main engines light up, followed by a deep roar a few seconds later, a huge grin spread across my face. But my expression soon changed to one of astonishment. What I had heard so far was merely the engines at intermediate thrust, when there’s a brief pause for a checkout. As the main engines opened up to full power, the noise engulfed me – a powerful rumble of deep bass notes that reverberated around my chest cavity. Just when I thought it couldn’t be any more impressive, the Soyuz lifted off the launch pad and, as it climbed, a deafening crackle filled the air.

My question is: what is intermediate thrust? And what is the brief pause before check out here for?

Does intermediate thrust means that the intermediate part try before starts and then they pause to check everything is okay before launch?

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The Soyuz launch sequence goes:

T-00:00:20  ENGINE IGNITION (Core Stage and Boosters)
T-00:00:20  Core Stage Umbilical Mast Retraction
T-00:00:15  Intermediate Thrust Level
T-00:00:10  Engine Turbopumps at Flight Speed
T-00:00:05  Full Thrust Level
T-00:00:00  Booster Umbilical Tower Retraction
T-00:00:00  LIFTOFF

The engines are running for 20 seconds before liftoff, which is a really long time. Roughly half of that is spent at an intermediate thrust level (hence lowered fuel and oxidizer consumption, reduced heat load on pad) before the last five seconds are at full thrust.

There's a SpaceFlight 101 article about an abort that says a bit more:

Soyuz goes through a 20-second ignition sequence leading up to liftoff, starting with the spin-up of the turbopumps before the engines throttle up to an intermediate thrust level for a brief checkout. Data monitored during the engine check period includes pressure and temperature in the chambers, pump speeds and vibration.

ArianeSpace isn't all that more specific:

Ignition of the central core and boosters occurs at an intermediate level of thrust on the launch pad 20 seconds before lift-off in order to monitor engine health parameters before the engines are throttled up and the vehicle leaves the pad.

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