
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
Define: For the function $f(x)$, if there exists a real number $x_{0}$ in the domain such that $f(-x_{0})=-f(x_{0})$, then $f(x)$ is called a "local odd function". If $f(x)=\frac{1}{{x-3}}+m$ is a "local odd function" defined on the interval $(-1,1)$, then the range of the real number $m$ is ____.

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