
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 doubling sum function is defined by
$$
D(a, n)=\overbrace{a+2 a+4 a+8 a+\ldots}^{n \text { terms }} .
$$

Determine the smallest positive integer \( n \) such that for every integer \( i \) between 1 and 6, inclusive, there exists a positive integer \( a_{i} \) such that \( D\left( a_{i}, i \right) = n \).

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