
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 $f\left(x-1\right)=|\log _{6}x|$, and the function $g\left(x\right)=f\left(x\right)-m\left(m \gt 0\right)$ has two intersection points with the $x$-axis. One of the intersection points has an $x$-coordinate of $\frac{1}{2}$. Find the $x$-coordinate of the other intersection point.

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