
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 there are 40 rods with lengths ranging from 1 cm to 40 cm, Joy initially selects rods of lengths 10 cm, 20 cm, and 30 cm. Then determine the number of remaining rods available for her to pick as her fourth rod from the table to form a quadrilateral with a nonzero area.

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