
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 that the real number $x$ satisfies the inequality $9^{x}-4×3^{x+1}+27\leqslant 0$ and the function $f(x)=(\log _{2} \dfrac {x}{2})(\log \;\_{ \sqrt {2}} \dfrac { \sqrt {x}}{2}).$

1. Find the range of values for $x$.
2. Find the maximum and minimum values of $f(x)$, and find the value of $x$ at these times.

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