
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
Find the best possible \( k, k' \) such that \( k < \frac{v}{v + w} + \frac{w}{w + x} + \frac{x}{x + y} + \frac{y}{y + z} + \frac{z}{z + v} < k' \) for all positive reals \( v, w, x, y, z \).

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