
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
Find the minimum value of the expression \(\frac{5 x^{2}+8 x y+5 y^{2}-14 x-10 y+30}{\left(4-x^{2}-10 x y-25 y^{2}\right)^{7 / 2}}\). If necessary, round your answer to the nearest hundredth.

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