
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 a circle C: \((x+2)^2 + y^2 = 5\), a line \(l: mx-y+1+2m=0\), where \(m \in \mathbb{R}\).
1. Determine the position relationship between the line and the circle, and explain the reason.
2. If the line \(l\) intersects the circle C at points A and B, find the equation of the locus of the midpoint M of chord AB.

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