
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
The dollar is now worth  $\frac{1}{980}$  ounce of gold. After the  $n^{th}$  7001 billion dollars bailout package passed by congress, the dollar gains  $\frac{1}{2{}^2{}^{n-1}}$  of its  $(n-1)^{th}$  value in gold. After four bank bailouts, the dollar is worth  $\frac{1}{b}(1-\frac{1}{2^c})$  in gold, where  $b, c$  are positive integers. Find  $b + c$ .

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