
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 constant numbers  $ u,\ v,\ s,\ t\ (s<t)$  such that  $ \int_{\minus{}1}^1 f(x)\ dx\equal{}uf(s)\plus{}vf(t)$  holds for any polynomials  $ f(x)\equal{}ax^3\plus{}bx^2\plus{}cx\plus{}d$  with the degree of 3 or less than.

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