
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
Joy has 50 thin rods, each of a unique integer length from 1 cm through 50 cm. She places rods with lengths 8 cm, 12 cm, and 20 cm on a table. She wants to choose two additional rods such that these five rods can form a polygon with positive area. Determine the number of pairs of the remaining rods that she can choose as the additional rods.

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