
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 \(\lfloor x \rfloor\) be the greatest integer not exceeding \( x \). For instance, \(\lfloor 3.4 \rfloor = 3\), \(\lfloor 2 \rfloor = 2\), and \(\lfloor -2.7 \rfloor = -3\). Determine the value of the constant \(\lambda > 0\) so that \(2\lfloor \lambda n \rfloor = 1 - n + \lfloor \lambda \lfloor \lambda n \rfloor \rfloor\) for all positive integers \(n\).

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