
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
Let \( f, g: \mathbf{Z}^{+} \rightarrow \mathbf{Z}^{+} \) be strictly increasing sequences such that \( f\left(\mathbf{Z}^{+}\right) \cap g\left(\mathbf{Z}^{+}\right) = \varnothing \) and \( f\left(\mathbf{Z}^{+}\right) \cup g\left(\mathbf{Z}^{+}\right) = \mathbf{Z}^{+} \). Given \( g(m) = f[f(m)] + 1 \), find \( f(2m) \).

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