
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 $f(x) = 1 + ae^{-x} + e^{-2x}$ and $g(x) = \log_{\frac{1}{2}} \frac{x+1}{mx-1}$,

1. Find the value of the real number $m$ if $g(x)$ is an odd function.
2. Under the condition of (1), find the set of all upper bounds of $g(x)$ on the interval $[\frac{9}{7}, 3]$.
3. If $f(x)$ is a bounded function with an upper bound of 3 on $[0, +\infty]$, find the range of values for the real number $a$.

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