
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
Suppose a binary operation $ \star$ has the properties that for all nonzero real numbers $a, b, c$, we have $a \star (b \star c) = (a \star b) \cdot c^2$ and $a \star a = 1$. Find the value of $x$ that satisfies $8 \star (4 \star x)=16$.

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