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

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

If the linear regression equation of $y$ and $x$ obtained by the method of least squares is $\hat{y}=2.1\hat{x}-0.3$, then $a=\_\_\_\_\_\_$.

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