
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 $y = f(x)$ be a linear function, where $f(0) = 1$ and $f(1)$, $f(4)$, $f(13)$ form a geometric progression. Find the value of $f(2) + f(4) + \dots + f(2n)$.

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