
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 $$f(x)= \begin{cases} (1-2a)x+5 & (x\leq 12) \\ a^{x-13} & (x>12) \end{cases}$$, if the sequence $\{a_n\}$ satisfies $a_n=f(n)$ for $n\in\mathbb{N}^+$, and for any two positive integers $m$, $n$ ($m\neq n$), $(m-n)(a_m-a_n)<0$ holds, then the range of values for the real number $a$ is \_\_\_\_\_.

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