
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
Given a set $T$ of $7$ integers taken from $\{1,2,\dots,20\}$ with the property that if $c$ and $d$ are elements of $T$ with $c<d$, then $d$ is not a multiple of $c$, and the sum of the least two elements of $T$ must be divisible by three, find the least possible value of an element in $T$.

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