
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]


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If for any positive numbers \( x \) and \( y \), the expressions \( a = x + y \), \( b = \sqrt{x^2 + xy + y^2} \), and \( c = m \sqrt{xy} \) form the side lengths of a triangle, then the range of values of the positive number \( m \) is \(\quad\).

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