
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
Let the complex number $z=4^m-1+(2^m+1)i$, where $m\in\mathbb{R}$. If the point corresponding to $z$ lies on the line $x-3y=0$, find the value of $m$.

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