
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 the scatter plot of a sample data group $((x\_1, y\_1), (x\_2, y\_2), ..., (x\_6, y\_6))$, if all sample points $(x\_i, y\_i) (i=1,2,...,6)$ oscillate near the curve $y=bx^2−\frac{1}{3}$. Given that $\sum\limits^{6 }\_{i\_=1 } x\_i=11$, $\sum\limits^{6 }\_{i\_=1 } y\_i=13$, and $\sum\limits^{6 }\_{i\_=1 } x^2\_i=21$, the value of the real number $b$ is $\_\_\_\_\_\_\_\_\_\_.$

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