
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 bag contains $4$ shiny coins and $3$ dull coins. One by one, coins are drawn at random from the bag and not replaced. You need to find the probability, expressed as a fraction $a/b$ in lowest terms, that it will take exactly six draws to see the third shiny coin appear. Calculate $a+b=$.
A) $7$
B) $9$
C) $11$
D) $13$
E) $15$

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