
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 \(ABCD\), \(AB=3\), \(AD=4\), point \(P\) is located on the plane of rectangle \(ABCD\) such that \(PA=2\) and \(PC=\sqrt{21}\). Find \(\overrightarrow{PB} \cdot \overrightarrow{PD}\).

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