
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 an exponential function $f\left(x\right)=a^{x}$ $(a \gt 0$, and $a\neq 1)$ passing through the point $\left(-2,9\right)$.  
$(1)$ Find the analytical expression of the function $f\left(x\right)$;  
$(2)$ If $f\left(2m-1\right)-f\left(m+3\right) \lt 0$, find the range of real numbers for $m$.

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