
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 $f(x) = m - \frac{2}{5^x + 1}$ defined on $\mathbb{R}$,  
(1) Determine the monotonicity of the function $f(x)$ \_\_\_\_\_\_;  
(2) If $f(x)$ is an odd function, find the value of $m$ \_\_\_\_\_\_;  
(3) If the range of $f(x)$ is $D$, and $D \subseteq [-3, 1]$, find the range of values for $m$ \_\_\_\_\_\_.

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