
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
For non-zero real numbers \( x, y, z, w \), if
$$
\frac{6 x y + 5 y z + 6 z w}{x^{2} + y^{2} + z^{2} + w^{2}} \leq f,
$$

find the minimum value of \( f \).

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