
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 the function $f(x) = \begin{cases} -x+6, & x\leq 2 \\ 3+\log_{a}x, & x > 2\end{cases}$ (where $a>0$ and $a\neq 1$),
1. If $a=2$, solve the inequality $f(x)\leq 5$.
2. If the range of the function $f(x)$ is $[4,+\infty)$, find the range of the real number $a$.

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