
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 triangle \( \triangle ABC \), let the sides opposite to angles \( \angle A \), \( \angle B \), and \( \angle C \) be \( a \), \( b \), and \( c \) respectively. Given that \( a^{2} + b^{2} = 2019c^{2} \), find:
$$
\frac{\cot C}{\cot A + \cot B}=
$$
\quad .

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