
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 set of sample data $(x_1, y_1)$, $(x_2, y_2)$, …, $(x_6, y_6)$, if all sample points $(x_i, y_i)$ $(i=1, 2, …, 6)$ fluctuate around the curve $y=bx^2 - \frac{1}{3}$. After calculation, $\sum\limits_{i=1}^{6}x_i=11$, $\sum\limits_{i=1}^{6}y_i=13$, $\sum\limits_{i=1}^{6}x_i^2=21$, then the value of the real number $b$ is \_\_\_\_\_\_.

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