
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 \\(P(x,y)\\) be any point on the curve \\(C\\): \\(\begin{cases}x=-2+\cos \theta \\ y=\sin \theta\end{cases} (\theta\\) as a parameter, \\(0 \leqslant \theta < 2\pi)\\),

  \\((1)\\) Convert the curve into a standard equation;

  \\((2)\\) Find the range of values for \\( \dfrac{y}{x} \\) and the range of values for \\(2x+y\\).

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