
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 standing to the right of a spool pulls the free end of the thread with a force \( F \) at an angle \(\alpha = 70^{\circ}\) to the horizontal. As a result, the spool rolls without slipping with a constant acceleration away from the person. At what angle to the horizontal should the person pull the thread with the same force so that the spool now rolls with the same acceleration towards the person? The spool's radii differ by a factor of two.

Answer: \( 48.8^{\circ} \) (it is also acceptable to specify the sine or cosine of this angle).

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