
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
The function \( f(x) \) defined on \( (-1,1) \) satisfies:
(1) For any \( x, y \in (-1,1) \), \( f(x) + f(y) = f\left(\frac{x+y}{1+xy}\right) \);
(2) When \( x \in (-1,0) \), \( f(x) > 0 \).

Compare the value of \( f\left(\frac{1}{5}\right) + f\left(\frac{1}{11}\right) + \cdots + f\left(\frac{1}{n^2 + 3n + 1}\right) \) with the value of \( f\left(\frac{1}{2}\right) \).

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