
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
Two lines intersect at point \(A\) at an angle not equal to \(90^\circ\); \(B\) and \(C\) are the projections of point \(M\) on these lines.

Find the angle between the line \(BC\) and the line passing through the midpoints of the segments \(AM\) and \(BC\).

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