
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 quadratic polynomial \( P(x) \) with the leading coefficient equal to 1 and the graph of \( y = P(x) \) marked at two points with abscissas 10 and 30. It is found that the bisector of the first quadrant of the coordinate plane intersects the segment between these points at its midpoint. Find \( P(20) \).

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