
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 person flips  $2010$  coins at a time. He gains one penny every time he flips a prime number of heads, but must stop once he flips a non-prime number. If his expected amount of money gained in dollars is  $\frac{a}{b}$ , where  $a$  and  $b$  are relatively prime, compute  $\lceil\log_{2}(100a+b)\rceil$ .

*Proposed by Lewis Chen*

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