
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, y) be a point on the graph of the function y = f(x), and let vectors $\overrightarrow {a}$ = ($1, {(x - 2)}^5$) and $\overrightarrow {b}$ = (1, y - 2x) be such that $\overrightarrow {a}$ is parallel to $\overrightarrow {b}$. Suppose that {a_n} is an arithmetic sequence with nonzero common difference, and that f(a_1) + f(a_2) + ... + f(a_9) = 36. Find the value of a_1 + a_2 + ... + a_9.

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