
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
Given \( a, b \in \mathbb{R} \). If for \( x \geqslant 0 \), it always holds that
\[ 
0 \leqslant x^{4} - x^{3} + ax + b \leqslant (x^{2} - 1)^{2}, 
\]
find the value of \( b - a \).

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