
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
A box contains $5$ shiny pennies and $5$ dull pennies. Pennies are drawn one by one at random from the box and are not replaced. If the probability is expressed as the ratio $a/b$ in its lowest terms that it will take exactly five draws for the third shiny penny to appear, compute $a+b$.
A) 17
B) 18
C) 19
D) 20
E) 21

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