
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 points A(3, 2) and B(-1, 5),
(1) Line $L_1$: $y=mx+2$ passes through the midpoint of segment AB. Find the value of $m$.
(2) If point C lies on line $L_1$ and the area of $\triangle ABC$ is 10, determine the coordinates of point C.

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