
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 $7$ dull pennies. One by one, pennies are drawn at random from the box without replacement. Find the probability, expressed as a simplified fraction $a/b$, that it will take more than five draws until the fourth shiny penny appears. Determine the value of $a+b$.
A) 45
B) 65
C) 71
D) 75
E) 81

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