
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
Joy has $50$ thin rods, each of different integer lengths ranging from $1$ cm to $50$ cm. She places rods of lengths $5$ cm, $10$ cm, and $20$ cm on a table. She wants to select a fourth rod so that the combination can form a quadrilateral with a positive area. How many rods from the remaining can she choose as the fourth rod?
A) 23
B) 24
C) 25
D) 26
E) 27

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