
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
When finding the minimum value of the function $y=x^{2}+ \frac{1}{x^{2}+a}\ (a > 0)$, a student's approach is as follows: According to the basic inequality, $y=x^{2}+ \frac{1}{x^{2}+a}=x^{2}+a+ \frac{1}{x^{2}+a}-a \geqslant 2 \sqrt{(x^{2}+a) \frac{1}{x^{2}+a}}-a = 2-a$. Therefore, the minimum value of the function $y=x^{2}+ \frac{1}{x^{2}+a}$ is $2-a$. If this student's solution is correct, the range of $a$ is _____.

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