
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
Define a function $f(x)$ on $\mathbb{R}$, such that for any real number $x \in \mathbb{R}$, it holds that $f(x+1) = f(x) + 1$, and $f(1) = 2$. Let $a_n = f(n)$ ($n \in \mathbb{N}^*$), then find the value of $a_{2010}$.

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