
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: $a \diamondsuit (b \diamondsuit c) = (a \diamondsuit b)^c$ and $a \diamondsuit a = 1$ for all nonzero real numbers $a, b,$ and $c$. Solve the equation $2048 \diamondsuit (4 \diamondsuit x) = 16$.

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