
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 $\{1, 2, 3, \dots, 100\}$, then $b$ is chosen from the same set at random. Calculate the probability that the integer $5^a + 6^b$ has units digit $0$.
A) $\frac{1}{25}$
B) $\frac{1}{10}$
C) $\frac{1}{50}$
D) $0$

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