
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 \( f(x) = \frac{1 + 10x}{10 - 100x} \). Set \( f^{n} = f \circ f \circ \cdots \circ f \). Find the value of
\[ f\left( \frac{1}{2} \right) + f^{2}\left( \frac{1}{2} \right) + f^{3}\left( \frac{1}{2} \right) + \cdots + f^{6000}\left( \frac{1}{2} \right). \]

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