
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
Observe the following three rows of numbers:<br/>$-2$,$4$,$-8$,$16$,$-32$,$\ldots $①<br/>$1$,$-2$,$4$,$-8$,$16$,$\ldots $②<br/>$3$,$6$,$12$,$24$,$48$,$\ldots $③<br/>$(1)$ The $6$th number in row ① is ______; the $7$th number in row ② is ______; the $7$th number in row ③ is ______;<br/>$(2)$ Given that $3072$ is one of the numbers, then it is the ______ number in the ______ row;<br/>$(3)$ Take the $n$th number from each row, if the sum of these three numbers is $32768$, find the value of $n$.

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