
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
Let $P$ be the foot of the perpendicular dropped from vertex $C$ of the smaller base $BC$ of an isosceles trapezoid $ABCD$ to its larger base $AD$. Find $DP$ and $AP$ if the bases of the trapezoid are $a$ and $b$ with $a > b$.

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