
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
Define a new operation $ \oplus $ by:
\[ a \oplus b = \frac{a + b}{1 + ab}. \]
Determine the value of:
\[ -1 \oplus (-2 \oplus (-3 \oplus (\dotsb \oplus (-999 \oplus -1000) \dotsb))). \]

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