
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
The sides of a parallelogram are \( a \) and \( b \) (\( a \neq b \)). At the vertices of the obtuse angles of this parallelogram, lines perpendicular to the sides were drawn. These lines intersect to form a parallelogram similar to the original one. Find the cosine of the acute angle of the given parallelogram.

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