
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 40 thin rods, one each of every integer length from 1 cm through 40 cm. She places on a table rods with lengths 5 cm, 10 cm, and 22 cm. What is the number of the remaining rods that she could choose as the fourth rod to form a quadrilateral with positive area?

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