
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 $f(x)$ be an odd function that is differentiable on $\mathbb{R}$, and $f'(x)$ is the derivative of $f(x)$. It is known that for $x > 0$, $f(x) < f'(x)$, and $f(1) = e$. The solution set of the inequality $0 < f(\ln(x+ \sqrt{1+x^{2}})) \leqslant e^{\ln(x+ \sqrt{1+x^{2}})}$ is denoted as $M$. Find the number of zeros of $g(x) = \sin 6x$ in the set $M$.

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