
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 a function $f(x)=\left\{\begin{array}{l}{x}^{2}-2ax-2,x\leq 2,\\ x+\frac{36}{x}-6a,x>2,\end{array}\right.$ If the minimum value of $f(x)$ is $f(2)$, determine the range of the real number $a$.

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