
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 of each integer length from $1 \text{ cm}$ to $40 \text{ cm}$. She selects rods of lengths $4 \text{ cm}$, $9 \text{ cm}$, and $18 \text{ cm}$ and lays them on the table. Joy seeks to find a fourth rod, which when combined with the previously chosen three, can form a valid quadrilateral with positive area. Determine how many of the remaining rods can be selected as the fourth rod.
A) 20
B) 21
C) 22
D) 23
E) 24

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