
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 regression line equation determined by a set of sample data is $\bar{y}=1.5x+1$, and $\bar{x}=2$, and two sets of data $(2.6,2.8)$ and $(1.4,5.2)$ have larger errors, find the estimated value of $\bar{y}$ when $x=6$ after the newly obtained regression line with a slope of $1.4$ is used.

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