
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
Any right triangle has the property that the sum of the areas of the squares on its two legs is equal to the area of the square on its hypotenuse. This is the famous Pythagorean theorem, also known in the West as the Pythagorean theorem. The Pythagorean theorem has a history of 4000 years, with hundreds of different proofs. The ancient Chinese mathematician Liu Hui from the Wei and Jin periods provided a concise and beautiful proof method shown in the left diagram below. The right diagram is the Liu Hui block puzzle based on this method:

The five blocks of the Liu Hui block puzzle can be assembled into the parallelogram shown on the right. If the right triangle's legs are 3 cm and 4 cm, what is the perimeter of the parallelogram in $\qquad$ centimeters?

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