
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 circle $C_{1}$: $\left(x+3\right)^{2}+y^{2}=2$ and parabola $C_{2}$: $y^{2}=4x$, please write down the equation of a line $l$ that has exactly one common point with both $C_{1}$ and $C_{2}$.

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