
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 pyramid \(ABCD\), the angle \( \angle ABC \) is \( \alpha \). Find the angle between the lines, one of which passes through the midpoints of the edges \(AC\) and \(BC\), and the other through the midpoints of the edges \(BD\) and \(CD\).

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