
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
You are given that \(x\) is directly proportional to \(y^3\), and \(y\) is inversely proportional to \(\sqrt{z}\). Further, \(z\) is directly proportional to \(w^2\). If the value of \(x\) is 8 when \(w\) is \(5\), what is the value of \(x\) when \(w\) is equal to \(10\)?

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