
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
Given two positive real numbers \( x \) and \( y \), the operation \( x \, \Diamond \, y \) is defined and satisfies \((x^2y) \, \Diamond \, y = x(y \, \Diamond \, y)\) and \((x \, \Diamond \, 1) \, \Diamond \, (x^2) = x \, \Diamond \, 1\) for all \( x,y > 0 \). Given that \( 1 \, \Diamond \, 1 = 1 \), find \( 5 \, \Diamond \, 49 \).

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