
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
In the same Cartesian coordinate system, given functions ${y_1}={x^2}+2x+c$ and $y_{2}=kx+2$ ($k$ is a non-zero constant). If the graph of function $y_{2}$ passes through the vertex of the graph of $y_{1}$, then the relationship between $k$ and $c$ is ______.

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