
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
(1) Given a point P(m, 1) on the terminal side of angle $\alpha$, and $\cos\alpha = -\frac{1}{3}$, find the value of $\tan\alpha$;  
(2) The perimeter of sector AOB is 8cm, and its area is 3cm<sup>2</sup>. Find the measure of the central angle.

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