
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 \( a \geqslant 3 \), the inequality \( \sqrt{a} - \sqrt{a-1} > \sqrt{a-2} - \sqrt{a-p} \) is always true. Find the range of values for \( p \) given that \( p > 2 \).

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