
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
Find the values of  $p,\ q,\ r\ (-1<p<q<r<1)$  such that for any polynomials with degree $\leq 2$ , the following equation holds:

\[\int_{-1}^p f(x)\ dx-\int_p^q f(x)\ dx+\int_q^r f(x)\ dx-\int_r^1 f(x)\ dx=0.\]

*1995 Hitotsubashi University entrance exam/Law, Economics etc.*

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