
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
Determine all real numbers  $a, b, c, d$  such that the polynomial  $f(x) = ax^3 +bx^2 + cx + d$  satisfies simultaneously the folloving conditions  $\begin {cases} |f(x)| \le 1 \,for \,  |x| \le 1  f(2) = 26 \end {cases}$ 

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