
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
Let \( x \) be directly proportional to \( y^3 \), and \( y \) be directly proportional to both \( \sqrt{z} \) and \( w \). Hence \( y = c \sqrt{z} w \) for some constant \( c \). Given that \( x = 5 \) when \( z = 8 \) and \( w = 1 \), determine \( x \) when \( z = 36 \) and \( w = 2 \).

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