
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 tetrahedron \(ABCD\), \(\triangle ABD\) is an equilateral triangle, \(\angle BCD = 90^\circ\), \(BC = CD = 1\), \(AC = \sqrt{3}\). Points \(E\) and \(F\) are the midpoints of \(BD\) and \(AC\) respectively. Determine the cosine of the angle between lines \(AE\) and \(BF\).

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