
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
For some constant  $k$  the polynomial  $p(x) = 3x^2 + kx + 117$  has the property that  $p(1) = p(10)$ . Evaluate  $p(20)$ .

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