
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
Given that a quadrilateral has positive area, determine the number of remaining rods that Joy can choose as the fourth rod, given that she has rods with lengths from 1 cm through 40 cm and has already placed rods of lengths 4 cm, 10 cm, and 22 cm on a table.

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