
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 measure of one angle of a parallelogram is $60^{\circ}$, and the shorter diagonal is $2 \sqrt{31}$ cm. The length of the perpendicular dropped from the intersection point of the diagonals to the larger side is $\sqrt{75} / 2 \mathrm{~cm}$. Find the lengths of the sides and the longer diagonal of the parallelogram.

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