
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
Positive integers \(a\), \(b\), and \(c\) are randomly and independently selected with replacement from the set \(\{1, 2, 3, \dots, 2023\}\). What is the probability that \(abc + ab + a\) is divisible by 3?
A) \(\frac{1}{3}\) \\
B) \(\frac{674}{2023}\) \\
C) \(\frac{2998}{18207}\) \\
D) \(\frac{9056}{18207}\) \\
E) \(\frac{1349}{2023}\)

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