
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 $\diamondsuit$ is defined such that $a \diamondsuit (b \diamondsuit c) = (a \diamondsuit b) \cdot c$ and $a \diamondsuit a = 1$ for all nonzero $a, b, c$. Solve the equation $504 \diamondsuit (3 \diamondsuit x) = 50$.

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