
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
In 2015, the epic historical drama "The Legend of Mi Yue" became a hit across China, rivaling the popularity of the previous drama "Empresses in the Palace." A journalist surveyed a large number of viewers of "The Legend of Mi Yue" and found that there was a relatively good linear relationship between age groups and the proportion of viewers who liked watching the show. The proportions of viewers who liked the show in the age groups \[10,14\], \[15,19\], \[20,24\], \[25,29\], and \[30,34\] were 10%, 18%, 20%, 30%, and $t\%$, respectively. Using the midpoint values $x$ to represent each age group, such as 12 for \[10,14\] and 17 for \[15,19\], and based on the first four data points, the linear regression equation of $x$ with respect to the proportion of viewers $y$ was found to be $\hat{y}=(kx-4.68)\%$. From this, we can infer the value of $t$.

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