
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 $f\left(x\right)=ax^{2}-x-1$, if the solution set of $f\left(x\right)\geqslant 0$ is $(-∞,-\frac{1}{2}]∪[1,+∞)$, find:<br/>$(1)$ the solution set of the inequality $f\left(x\right)\leqslant 1-x^{2}$;<br/>$(2)$ the range of real number $m$ if $f\left(\ln x\right)+5 \gt m\ln x$ holds for all $x\in [e$,$e^{2}]$.

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