
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 $a$ and $b$ be real numbers. Determine the ordered pair $(a,b)$ such that one of the roots of the polynomial 
\[x^3 + ax^2 + 6x + b = 0\]
is $1 - 3i$.

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