
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 that \( f(x) \) is a function defined on \( \mathbf{R} \), with \( f(1) = 1 \) and for any \( x \in \mathbf{R} \) the inequalities \( f(x+5) \geq f(x) + 5 \) and \( f(x+1) \leq f(x) + 1 \) hold. If \( g(x) = f(x) + 1 - x \), then \( g(2002) = \) .

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