
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 $4$ shiny pennies and $5$ dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is $a/b$ that it will take more than five draws until the third shiny penny appears and $a/b$ is in lowest terms, then calculate $a+b=$.
A) 90
B) 95
C) 100
D) 105
E) 110

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