
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
Using the same binary operation $\diamondsuit$ defined by $a\,\diamondsuit\, (b\,\diamondsuit \,c) = (a\,\diamondsuit \,b)\cdot c$ and $a\,\diamondsuit \,a=1$ for all nonzero real numbers $a, b,$ and $c$, solve the equation $504 \,\diamondsuit\, (12\,\diamondsuit\, x)=50.$

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