
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 $a$, $b$, $c$, and $d$ are randomly and independently selected with replacement from the set $\{1, 2, 3,\dots, 100\}$. What is the probability that $abcd + abc + ab + a$ is divisible by $3$?
A) $\frac{1}{3}$  
B) $\frac{29}{81}$  
C) $\frac{31}{81}$  
D) $\frac{11}{27}$  
E) $\frac{43}{100}$

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