
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
When \(2x^2\) is added to a quadratic polynomial \(f(x)\), its maximum value increases by 10, and when \(5x^2\) is subtracted from it, its maximum value decreases by \(\frac{15}{2}\). By how much will the maximum value of \(f(x)\) change if \(3x^2\) is added to it?

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