
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
Lia has a collection of 40 thin rods, each of a unique length from 1 cm to 40 cm. She selects rods of lengths 5 cm, 10 cm, and 20 cm and places them on the table. Lia wants to choose a fourth rod so that together, they can form a quadrilateral with a positive area. How many of the remaining rods can she use as the fourth rod?
A) 24
B) 25
C) 26
D) 27
E) 28

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