
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 point $O$ be the origin, and the coordinates of points $A$ and $B$ be $(a, 0)$ and $(0, a)$ respectively, where $a$ is a positive constant. Point $P$ lies on segment $AB$, and $\overrightarrow{AP} = t \cdot \overrightarrow{AB}$ for $0 \leq t \leq 1$. Find the maximum value of $\overrightarrow{OA} \cdot \overrightarrow{OP}$.

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