
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 Joy has 40 thin rods, one each of every integer length from 1 cm through 40 cm, with rods of lengths 4 cm, 9 cm, and 18 cm already placed on a table, determine how many of the remaining rods can be chosen as the fourth rod to form a quadrilateral with positive area.

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