
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 $f(x)=-\frac{1}{x}+x$, $g(x)=x^2-4x-3$, if for all $x_{1}\in \left[-2,-1\right]$, there exists $x_{2}\in \left[1,a\right]$, such that $f(x_{1}) \lt g(x_{2})$ holds, then the range of real number $a$ is ______.

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