
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 $30$ thin rods, each of every integer length from $1 \text{ cm}$ through $30 \text{ cm}$. She selects rods with lengths $4 \text{ cm}$, $9 \text{ cm}$, and $17 \text{ cm}$ and places them on a table. She wants to choose a fourth rod that can be combined with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
A) 20
B) 21
C) 22
D) 23 
E) 24

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