
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 5 integers taken from $\{2,3, \dots, 15\}$ such that if $c$ and $d$ are elements of $T$ with $c<d$, then $d$ is not a divisor of $c$, determine the greatest possible value of an element in $T$.

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