
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 $a \gt 0$ and $a\neq 1$, if the range of the function $f(x)=\left\{\begin{array}{l}-x+7, x≤2\\ 3+\log_{a}x, x>2\end{array}\right.$ is $\left[5,+\infty \right)$, determine the range of values for $a$.

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