
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 $\{1, 2, 3,\dots, 5000\}$. What is the probability that $abc + ab + a$ is divisible by $4$?
A) $\frac{15}{64}$
B) $\frac{25}{64}$
C) $\frac{1}{4}$
D) $\frac{35}{64}$
E) $\frac{45}{64}$

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