
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 that the average of the data $x_1$, $x_2$, $x_3$ is $a$, and the average of the data $y_1$, $y_2$, $y_3$ is $b$, calculate the average of the data $2x_1+3y_1$, $2x_2+3y_2$, $2x_3+3y_3$.

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