
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 $40$ thin rods, one each of every integer length from $1 \text{ cm}$ through $40 \text{ cm}$. She places the rods with lengths $5 \text{ cm}$, $12 \text{ cm}$, and $20 \text{cm}$ on a table. She wants to choose a fourth rod so that along with these three, it is possible to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
A) 28
B) 29
C) 30
D) 31
E) 32

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