
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  $ABCD$ , side  $AB$  is longer than side  $BC$ . Find all the points  $P$  of the side line  $AB$  from which the sides  $AD$  and  $DC$  are seen from the point  $P$  at an equal angle (i.e.  $\angle APD = \angle DPC$ )

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