
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
The polar coordinate system and the rectangular coordinate system $(xOy)$ have the same unit of length. The origin $(O)$ is the pole, and the positive semi-axis of the $x$-axis is the polar axis $(.)$. The polar coordinate equation of the curve $C_{1}$ is $ρ-2\cos θ=0$, and the parametric equation of the curve $C_{1}$ is $ \begin{cases}x=t+m \\\\ y=2t-1\end{cases}(t)$ is the parameter, $(m)$ is a constant$()$
$((\text{I})())$ Find the rectangular coordinate equation of $C_{1}$ and the ordinary equation of $C_{2}$;
$((\text{II})())$ If $C_{2}$ and $C_{1}$ have two different common points, find the range of values of $m$.

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