
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

Let the plane vectors $\boldsymbol{a}$ and $\boldsymbol{b}$ satisfy: $|\boldsymbol{a}|=1$, $|\boldsymbol{b}|=2$, and $\boldsymbol{a} \perp \boldsymbol{b}$. Points $O$, $A$, and $B$ are three points on the plane, satisfying $\overrightarrow{OA} = 2\boldsymbol{a} + \boldsymbol{b}$ and $\overrightarrow{OB} = -3\boldsymbol{a} + 2\boldsymbol{b}$. Find the area of triangle $\triangle AOB$.

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