
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 the function \( f(x) \) defined on \( \mathbf{R} \) with \( f(1)=1 \), and for any \( x \in \mathbf{R} \), the conditions \( f(x+5) \geqslant f(x)+5 \) and \( f(x+1) \leqslant f(x)+1 \) hold. If \( g(x)=f(x)+1-x \), find the value of \( g(2002) \).

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