
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
Answer the following questions as required.
1. Given $10^{m}=12$ and $10^{n}=3$, find the value of $10^{m-n}$.
2. If $a+3b=3$, find the value of $3^{a}\times 27^{b}$.
3. Given $8\times 2^{m}\div 16^{m}=2^{6}$, find the value of $m$.

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