
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
For which values of the obtuse angle \( \gamma \) is the following statement true: If one of the angles of a triangle is \( \gamma \), then

\[ \frac{T}{\sqrt{a^2 b^2 - 4T^2}} + \frac{T}{\sqrt{b^2 c^2 - 4T^2}} + \frac{T}{\sqrt{c^2 a^2 - 4T^2}} \geq \frac{3\sqrt{3}}{2} \]

where \( a, b, c \) are the sides of the triangle, and \( T \) is the area of the triangle.

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