
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 that the odd function $f(x)$ defined on $\mathbb{R}$ satisfies the inequality $f(x+m) < f(x)$ when $x \geq 0$ and $m > 0$, if the inequality $f(2e^x - ax) - f(e^x + b) \leq 0$ holds for any $x \in \mathbb{R}$ (where $a > 0$, $b \in \mathbb{R}$), determine the maximum value of $ab$.

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