
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 \(b\), and the angle between them is \(\alpha\). Find the sides and the diagonals of the quadrilateral formed by the intersection of the angle bisectors of the internal angles of the parallelogram.

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