
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
A binary operation \(\diamondsuit\) has properties that \(a\,\diamondsuit\, (b\,\diamondsuit \,c) = (a\,\diamondsuit \,b)\cdot c\) and that \(a\,\diamondsuit \,a=1\) for all nonzero real numbers \(a, b,\) and \(c\). Find the solution to the equation \(504 \,\diamondsuit\, (3\,\diamondsuit\, x)=50.\)

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