
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 $f(x) = \frac{e^x - e^{-x}}{2}$, where $x \in \mathbb{R}$, for any $\theta \in (0, \frac{\pi}{2}]$, find the range of the real number $m$ such that the inequality $f(m\sin\theta) + f(1-m) > 0$ holds.

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