
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
The cubic polynomial \( q(x) \) satisfies \( q(1) = 8, \) \( q(9) = 40, \) \( q(17) = 16, \) and \( q(25) = 56. \) Find
\[
q(0) + q(1) + q(2) + \dots + q(26).
\]

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