
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 a function $f(x)$ defined on $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ is an odd function, and when $x \in \left(0, \frac{\pi}{2}\right)$, $f(x) = \frac{\tan x}{\tan x + 1}$.

(1) Find the expression of $f(x)$ on the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

(2) For what value of the real number $m$ does the equation $f(x) = m$ have a solution in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$?

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