
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 $x$, $f(x+3) \leq f(x) + 3$ and $f(x+2) \geq f(x) + 2$, and $f(1) = 1$. Then, calculate the value of $f(2005)$.

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