
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 $f(x)$ be a linear function, given that $f(8) = 15$, and $f(2), f(5), f(4)$ form a geometric sequence,

(1) Find the expression for $f(x)$;  
(2) Find the sum of $f(2) + f(4) + f(6) + \cdots + f(2n)$.

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