
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 O is the origin, and the coordinates of points A and B are (a,0) and (0,a) respectively, where the constant a > 0, point P is on the line segment AB, and  \overrightarrow{AP}=t \overrightarrow{AB} (0 ≤ t ≤ 1), calculate the maximum value of  \overrightarrow{OA} ⋅ \overrightarrow{OP}.

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