
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
Read the following program:  
INPUT x  
IF x < 0 THEN  
y = x*x - 2*x + 6  
ELSE  
y = (x-1)*(x-1)  
END IF  
PRINT y  
END  
If the output y = 9, then the input value of x should be __________.

For the inequality about x, $x(1-x) < a(1-a)$ ($a < 0$), the solution set is __________.

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