
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
Given the function $f(x) = a\sin(\pi x + \alpha) + b\cos(\pi x + \beta) + 4$, where $\alpha$, $\beta$, $a$, and $b$ are non-zero real numbers, and $f(2003) = 6$, then the value of $f(2004)$ is.

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