
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 that $\triangle ABC$ is an isosceles right triangle with $\angle A=90^{\circ}$, and $\overrightarrow{AB}=\boldsymbol{a}+\boldsymbol{b}$, $\overrightarrow{AC}=a-b$. If $a=(\cos \theta, \sin \theta)$ where $\theta \in \mathbf{R}$, then the area of $\triangle ABC$ is equal to $\qquad$.

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