
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A boy presses with his thumb along a vertical rod resting on a rough horizontal surface. Then he gradually starts tilting the rod while keeping the force component along the rod constant. When the angle of tilt of the rod to the horizontal is $\alpha = 70^{\circ}$, the rod begins to slide on the surface. Determine the coefficient of friction between the surface and the rod, if in the vertical position, the reaction force of the surface was 21 times the gravitational force acting on the rod. Round the answer to two decimal places.

Present the answer in LaTex format: \boxed{Your answer}
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