
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 $f(x) = \begin{cases} (a-1)x+4, & x\leq 7 \\ a^{x-6}, & x>7 \end{cases}$;  
(1) When $a= \frac {1}{2}$, the range of $f(x)$ is \_\_\_\_\_\_ ,  
(2) If $f(x)$ is a decreasing function on $(-\infty, +\infty)$, then the range of the real number $a$ is \_\_\_\_\_\_ .

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