
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
Let $p(x)$ be a monic quartic polynomial such that $p(2) = 7,$ $p(3) = 12,$ $p(4) = 19,$ and $p(5) = 28.$ Find $p(6).$

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