
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 $f(x) = m\sin(\pi x + \alpha_1) + n\cos(\pi x + \alpha_2)$, where $m$, $n$, $\alpha_1$, and $\alpha_2$ are all non-zero real numbers. If $f(2011) = 1$, then $f(2012) = \ $.

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