
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
In rectangle \(ABCD\), \(AD = 10\), \(CD = 15\), \(P\) is a point inside the rectangle such that \(PB = 9\), \(PA = 12\). Find \( \overline{P} \).

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