
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
Italian painter Leonardo da Vinci pondered a question while creating "Lady with an Ermine": what curve is formed by the long necklace worn by the woman in the painting? This is the famous "catenary problem." After choosing a suitable coordinate system, the equation of the catenary is the hyperbolic cosine function $cosh(x)=\frac{{{e^x}+{e^{-x}}}}{2}$, and similarly, there is the hyperbolic sine function $sinh(x)=\frac{{{e^x}-{e^{-x}}}}{2}$. Therefore, $\left[\cos h\left(x\right)\right]^{2}-\left[\sinh \left(x\right)\right]^{2}=\_\_\_\_\_\_$. Let $f\left(x\right)=\sinh \left(x\right)\cdot \cos h\left(x\right)$, then the solution set of the inequality $f(x)＜\frac{{1-{e^4}}}{{4{e^2}}}$ is ______.

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