
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
Find the period of the repetend of the fraction  $\frac{39}{1428}$  by using *binary* numbers, i.e. its binary decimal representation.

(Note: When a proper fraction is expressed as a decimal number (of any base), either the decimal number terminates after finite steps, or it is of the form  $0.b_1b_2\cdots b_sa_1a_2\cdots a_ka_1a_2\cdots a_ka_1a_2 \cdots a_k \cdots$ . Here the repeated sequence  $a_1a_2\cdots a_k$  is called the *repetend* of the fraction, and the smallest length of the repetend,  $k$ , is called the *period* of the decimal number.)

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