
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 vertically along a rod standing on a rough horizontal surface with his thumb. He then starts gradually tilting the rod, maintaining the component of force directed along the rod constant. At an inclination angle of the rod to the horizontal of $\alpha=75^{\circ}$, the rod starts to slide on the surface. Determine the coefficient of friction between the surface and the rod, given that in the vertical position the normal force exerted by the surface is 16 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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