
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
An isosceles trapezoid with bases \(a\) and \(b\) and height \(h\) is given.
(a) On the line of symmetry, construct the point \(P\) such that both (nonbase) sides are seen from \(P\) with an angle of \(90^{\circ}\).
(b) Find the distance of \(P\) from one of the bases of the trapezoid.
(c) Under what conditions for \(a\), \(b\), and \(h\) can the point \(P\) be constructed (analyze all possible cases)?

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