
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
Given that \( x, y, z \in \mathbb{R}_{+} \), and \( s = \sqrt{x+2} + \sqrt{y+5} + \sqrt{z+10} \), \( t = \sqrt{x+1} + \sqrt{y+1} + \sqrt{z+1} \), find the minimum value of \( s^{2} - t^{2} \).

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