
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 \( x \star y = \frac{\sqrt{x^2 + 3xy + y^2 - 2x - 2y + 4}}{xy + 4} \). Compute
\[ ((\cdots((2007 \star 2006) \star 2005) \star \cdots) \star 1) . \]

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