
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 $f(x)=a^{x}$ ($a > 0$, $a \neq 1$) with a maximum value of $4$ on $[-1,2]$ and a minimum value of $m$, and the function $g(x)=(1-4m) \sqrt {x}$ is an increasing function on $[0,+\infty)$, find the value of $a$.

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