
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
The square of $a$ and the fourth root of $c$ vary inversely. When $a = 3$ and $c = 256$, the product of $a$ and $c$ equals $768$. Find the value of $c$ when $a = 4$.

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