
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 $X$ be a random variable such that $\mathrm{E} e^{s X}<\infty$, $s \in \mathbb{R}$ and

$$
\int_{\mathbb{R}}\left|\mathrm{E} e^{(s+i t) X}\right| d t<\infty, \quad s, t \in \mathbb{R}
$$

The last condition for $s=0$ guarantees the existence of the density $f=f(x)$ of $X$. Under these conditions, suggest a method for obtaining upper bounds for $f$ on $\mathbb{R}$.

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