
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 functions $f(x)=\frac{1}{2}a{x^2}-lnx-1$ and $g\left(x\right)=e^{x}-ax$ have the same minimum value.<br/>$(1)$ Find the value of the real number $a$;<br/>$(2)$ Find the solution set of the inequality ${e^x}-\frac{{a{x^2}}}{{1+lnx}}＜0$.

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