
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 $O$ be the coordinate origin and $P$ be the point with coordinates $(2,1)$. If $A$ and $B$ are points on the positive semi-axes of the $x$-axis and $y$-axis respectively such that $PA \perp PB$, find the maximum area of $\triangle OAB$.

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