
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
Source: 2018 Canadian Open Math Challenge Part B Problem 3
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The *doubling sum* function is defined by
\[D(a,n)=\overbrace{a+2a+4a+8a+...}^{\text{n terms}}.\]
For example, we have
\[D(5,3)=5+10+20=35\]
and
\[D(11,5)=11+22+44+88+176=341.\]
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  $D(a_i,i)=n.$ 

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