
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
Isosceles trapezoid \(ABCD\) with bases \(AB\) and \(CD\) has a point \(P\) on \(AB\) with \(AP = 11\), \(BP = 27\), \(CD = 34\), and \(\angle CPD = 90^\circ\). Compute the height of isosceles trapezoid \(ABCD\).

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