
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
In an isosceles triangle $ABC$ with a perimeter of 6, when the vertex angle $A = \frac{\pi}{3}$, the maximum value of the area of $\triangle ABC$ is $\sqrt{3}$. In a sector $OAB$ with a perimeter of 4, when the central angle $\alpha$, $|\alpha| = \angle AOB = \_\_\_\_\_\_$ (in radians), the maximum value of the area of sector $OAB$ is 1.

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