
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
For any positive real number \( x \), \(\lfloor x \rfloor\) denotes the largest integer less than or equal to \( x \), where \( x > 0 \). If \(\lfloor x \rfloor \cdot x = 36\) and \(\lfloor y \rfloor \cdot y = 71\), determine the value of \( x + y \).

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