
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 the function $f(x) = (x-3)^3 + x - 1$, and $\{a_n\}$ be an arithmetic sequence with a non-zero common difference. If $f(a_1) + f(a_2) + \ldots + f(a_7) = 14$, then calculate the value of $a_1 + a_2 + \ldots + a_7$.

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