
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 of each integer length from 1 cm to 40 cm. She places rods of lengths 4 cm, 8 cm, and 17 cm on a table. She wants to select one more rod to form a quadrilateral with a positive area. How many of the remaining rods can be used for this purpose?
A) 18
B) 19
C) 20
D) 21
E) 22

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