
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
Suppose \(a, b\), and \(c\) are real numbers such that
\[ 
\begin{aligned}
a^{2} - bc &= 14, \\
b^{2} - ca &= 14, \\
c^{2} - ab &= -3.
\end{aligned} 
\]
Compute \(|a + b + c|\).

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