
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 a number \( a \in (0,1) \). Positive numbers \( x_{0}, x_{1}, \ldots, x_{n} \) satisfy the conditions \( x_{0} + x_{1} + \ldots + x_{n} = n + a \) and \( \frac{1}{x_{0}} + \frac{1}{x_{1}} + \ldots + \frac{1}{x_{n}} = n + \frac{1}{a} \). Find the minimum value of the expression \( x_{0}^{2} + x_{1}^{2} + \ldots + x_{n}^{2} \).

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