
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
Liam has 25 thin rods, each one having a unique integer length from 1 cm to 25 cm. He places rods of lengths 4 cm, 9 cm, and 18 cm on a table. He wants to select an additional rod that can be used with these three to form a quadrilateral with a positive area. Determine how many of the remaining rods Liam can choose as the fourth rod.
A) 15
B) 16
C) 17
D) 19
E) 20

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