
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 the linear regression line equation $\widehat{y}=\widehat{b}x+\widehat{a}$, $\sum\limits_{i=1}^{10}{x_i}=225$, $\sum\limits_{i=1}^{10}{y_i}=1600$, and $\overline{b}=4$, derive the equation of the regression line and then determine the estimated height $\widehat{y}$ for a student whose foot length is $x=24$ cm.

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