
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 $6$ 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 six draws until the fourth shiny penny appears and $a/b$ is in lowest terms, then find $a+b$.
A) 372
B) 386
C) 400
D) 415
E) 435

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