
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 $f(x)=\frac{1}{8}(m-1){x}^{2}-mx+2m-1$.

(1) For what value(s) of $m$ does the graph of the function have only one point in common with the $x$-axis?

(2) If one of the zeros of the function is $2$, find the value of $m$ and the other zero of the function.

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