
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]


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In the rectangular coordinate system $(xOy)$, establish a polar coordinate system with the origin $O$ as the pole, the non-negative semi-axis of $x$ as the polar axis, and the same length unit as the rectangular coordinate system $(xOy)$. Given that the polar coordinate equation of curve $C_{1}$ is $ρ=2\cos θ$ and the parametric equation of curve $C_{2}$ is $\begin{cases} x=-\frac{4}{5}t \\ y=-2+\frac{3}{5}t\end{cases}$ (where $t$ is the parameter),

1. Determine the positional relationship between curves $C_{1}$ and $C_{2}$;
2. If $M(x, y)$ is any point on curve $C_{1}$, find the range of values for $x+y$.

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