
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 that $y$ is a quadratic function of $x$, the table below shows some corresponding values of $y$ and $x$:<br/>

| $x$ | $\ldots $ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | $\ldots $ |
|-----|-----------|------|------|----|----|----|----|----|----------|
| $y$ | $\ldots $ | $11$ | $a$  | $3$ | $2$ | $3$ | $6$ | $11$| $\ldots $ |

Based on this, it can be concluded that $a=$____.

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