
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 certain extracurricular interest group conducted a survey on the reading of classic literature among people of different age groups in a certain area. The relevant data is shown in the table below:

| Age Interval (years) | $[0,10)$ | $[10,15)$ | $[15,20)$ | $[20,25)$ | $[25,30)$ |
|----------------------|----------|-----------|-----------|-----------|-----------|
| Variable $x$         | $1$      | $2$       | $3$       | $4$       | $5$       |
| Population $y$       | $2$      | $3$       | $7$       | $8$       | $a$       |

According to the data in the table, the population $y$ is linearly related to the variable $x$, and the relationship is given by $\hat{y}=2.1x-0.3$. Find the value of $a$.

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