
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 that $a > 1$, the difference between the maximum value $M$ and the minimum value $m$ of the function $y=\log_{a}x$ in the closed interval $[3,6]$ is equal to $1$.

1. Find the value of $a$;
2. Compare the size of $3^{M}$ and $6^{m}$.

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