
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 a function \( f(x) \) defined on \(\mathbf{R}\), where \(f(1)=1\) and for any \( x \in \mathbf{R} \)
\[ 
\begin{array}{l}
f(x+5) \geq f(x) + 5 \\
f(x+1) \leq f(x) + 1
\end{array}
\]
If \( g(x) = f(x) + 1 - x \), then \( g(2002) = \)

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