
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 pairs of real numbers  $(a,b)$  such that the biggest of the numbers  $x=b^2-\frac{a-1}{2}$  and  $y=a^2+\frac{b+1}{2}$  is less than or equal to  $\frac{7}{16}$ 

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