
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
1. Find the coordinates of the point on the z-axis that is equidistant from point A (-4, 1, 7) and B (3, 5, -2).
2. In the yOz plane, find the coordinates of the point that is equidistant from points A (3, 1, 2), B (4, -2, -2), and C (0, 5, 1).

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