
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
Let the ordered triples $(a,b,c)$ of complex numbers that satisfy
\begin{align*}
a + bc &= 9, \\
b + ac &= 15, \\
c + ab &= 15.
\end{align*}
be $(a_1,b_1,c_1),$ $(a_2,b_2,c_2),$ $\dots,$ $(a_n,b_n,c_n).$  Find $a_1 + a_2 + \dots + a_n.$

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