
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 \( f(x) = \frac{2}{4^x + 2} + 2 \), find the sum \( f\left(\frac{1}{m}\right) + f\left(\frac{2}{m}\right) + \cdots + f\left(\frac{m-1}{m}\right) \) where \( m \geq 2 \) and \( m \in \mathbf{N} \).

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