
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
Given \(\boldsymbol{a} = \left(\cos \frac{2}{3} \pi, \sin \frac{2}{3} \pi\right), \overrightarrow{O A} = \boldsymbol{a} - \boldsymbol{b}, \overrightarrow{O B} = \boldsymbol{a} + \boldsymbol{b},\) if \(\triangle O A B\) is an isosceles right triangle with \(O\) as the right-angle vertex, then the area of \(\triangle O A B\) is _____

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