
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
A side of the base of a regular quadrilateral prism is equal to \(a\), and its volume is \(V\). Find the cosine of the angle between the diagonals of two adjacent lateral faces.

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