
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 a rectangle \(ABCD\), where \(AB\) is the shorter side, determine for which points \(P\) on the line \(AD\) the angle bisector of \(\angle BPD\) passes through point \(C\). Justify your claim and describe how you would construct all such points.

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