
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 $q(5) = 2,$ $q(10) = 22,$ $q(15) = 12,$ and $q(25) = 32.$ Find
\[
q(4) + q(5) + q(6) + \dots + q(26).
\]

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