
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
First \(a\) is chosen at random from the set \(\{1,2,3,\dots,99,100\}\), and then \(b\) is chosen at random from the same set. The probability that the integer \(2^a+5^b\) has a units digit of \(8\) is
A) 0
B) \(\frac{1}{4}\)
C) \(\frac{1}{8}\)
D) \(\frac{1}{16}\)
E) \(\frac{1}{20}\)

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