
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 person on the right side of a spool of thread pulls its free end with a force \( F \) at an angle \(\alpha = 20^\circ\) to the horizontal. As a result, the spool rolls without slipping with a constant acceleration toward the person. At what angle to the horizontal should the person pull the thread with the same force, so the spool now rolls with the same acceleration away from them? The spool's radii differ by a factor of two.

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