
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 the diagram below, the lengths of the three sides of the triangle are \(a \text{ cm}, b \text{ cm}\) and \(c \text{ cm}\). It is given that \(\frac{a^{2}+b^{2}}{c^{2}}=2011\). Find the value of \(\frac{\cot C}{\cot A + \cot B}\).

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