
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 domain of functions $f(x)$ and $g(x)$ be $\mathbb{R$, and both have inverse functions. The graphs of $f(x-1)$ and $g^{-1}(x-2)$ are symmetric about the line $y=x$. If $g(5)=2004$, then find $f(4)$.

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