
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
Isaac repeatedly flips a fair coin. Whenever a particular face appears for the  $2n+1$ th time, for any nonnegative integer  $n$ , he earns a point. The expected number of flips it takes for Isaac to get  $10$  points is  $\tfrac ab$  for coprime positive integers  $a$  and  $b$ . Find  $a + b$ .

*Proposed by Isaac Chen*

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