
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 power function $y=f(x)$ passes through the points $(8, m)$ and $(9, 3)$.
(1) Find the value of $m$;
(2) If the function $g(x)=\log_{a}f(x)$ has its maximum value 1 greater than its minimum value on the interval $[16, 36]$, find the value of the real number $a$.

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