
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 continuous function  $ f(x)$  satisfies that  $ \frac {d}{dx}\left(\int_0^x f(x \plus{} t)\ dt \right)\equal{} 0$ . Find the necessary and sufficient condition such that  $ \sum_{n \equal{} 1}^{\infty} f(2^n) \equal{} 1$ .

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