
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
Distinct positive numbers \(a, b, c\) satisfy the following system of equations:

\[
\left\{
\begin{array}{l}
a^{2} + bc = 115 \\
b^{2} + ac = 127 \\
c^{2} + ab = 115
\end{array}
\right.
\]

Find \(a + b + c\).

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