
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
 $(a)$  Let  $x, y$  be integers, not both zero. Find the minimum possible value of  $|5x^2 + 11xy - 5y^2|$ . $(b)$  Find all positive real numbers  $t$  such that  $\frac{9t}{10}=\frac{[t]}{t - [t]}$ .

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