
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
Solve the boundary value problem \(x^{2} y^{\prime \prime} + 2x y^{\prime} - 6y = 0\), given \(y(1) = 1\), and \(y(x)\) is bounded as \(x \rightarrow 0\).

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