
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 tetrahedron \(A B C D\), where \(B D = D C = C B = \sqrt{2}\), \(A C = \sqrt{3}\), and \(A B = A D = 1\), find the cosine of the angle between line \(B M\) and line \(A C\), where \(M\) is the midpoint of \(C D\).

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