
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 that the function $y=f\left(x\right)$ is an even function, and for any $x_{1}$, $x_{2}\in \left[0,+\infty \right)$ $(x_{1}\neq x_{2})$, $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}＜0$. If $f\left(a+2\right) \gt f\left(a-3\right)$, determine the range of real number $a$.

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