
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
A student analyzed the data of the heights $y$ (unit: cm) and shoe sizes $x$ (unit: European size) of 50 classmates and found that they were linearly related. The student obtained the empirical regression equation $\hat{y}=3x+\hat{a}$. If the average height and shoe size of the 50 classmates are $\overline{y}=170$ and $\overline{x}=40$ respectively, then $\hat{a}=\_\_\_\_\_\_$.

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