
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 a scatter plot 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 $y=bx^{2}-1$. Given that $\sum\limits_{i=1}^{6}x_{i}=11$, $\sum\limits_{i=1}^{6}y_{i}=13$, and $\sum\limits_{i=1}^{6}x_{i}^{2}=21$, determine the value of the real number $b$.

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