
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 \( f(x) = \left( e^x - e^{-x} \right) \cdot x^3 \), if \( m \) satisfies \( f\left(\log_2 m\right) + f\left(\log_{0.5} m\right) \leq 2 \left(\frac{e^2 - 1}{e}\right) \), find the range of the real number \( m \).

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