
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 two sets of data $(x\_1)$, $(x\_2)$, ..., $(x\_n)$ and $(y\_1)$, $(y\_2)$, ..., $(y\_n)$ with respective means $\overline{x}$ and $\overline{y}$, find the mean of the new set of data $(2x\_1 - 3y\_1 + 1)$, $(2x\_2 - 3y\_2 + 1)$, ..., $(2x\_n - 3y\_n + 1)$.

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