
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
Given a cubic polynomial $q(x)$ that satisfies $q(1) = 5$, $q(6) = 24$, $q(10) = 16$, and $q(15) = 34$, find the sum $q(0) + q(1) + q(2) + \dots + q(16)$.

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