
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 two positive real numbers $m$ and $n$, set $a = m + n$ and $b = \sqrt{m^2 + 14mn + n^2}$. If $a$ and $b$ are the lengths of two sides of a certain triangle, and the length of the third side is $c$, which satisfies $c^2 = k \cdot mn$, find the range of the real number $k$.

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