
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
$(1)$ Calculate: $2\tan 60^{\circ}\cos 30^{\circ}-\sin ^{2}45^{\circ}$;<br/>$(2)$ Solve the equation: $2\left(x+2\right)^{2}-3\left(x+2\right)=0$;<br/>$(3)$ If $m$ is a real root of the quadratic equation $x^{2}-5x-2=0$, find the value of $2m^{2}-10m+2023$.

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