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

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