
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 $f(x) = a\sin(\pi x + \alpha) + b\cos(\pi x + \beta)$, where $a, b, \alpha, \beta \in \mathbb{R}$, and $ab \neq 0$, $\alpha \neq k\pi$ ($k \in \mathbb{Z}$). Find the value of $f(2010)$.

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