
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 the function $f(x)=|x+a|-|x-a^2-a|$ where $a \in \mathbb{R}$.
- (I) When $a=1$, find the solution set of the inequality $f(x) \leqslant 1$.
- (II) If for any $a$ in the interval $[-1, \frac{1}{3}]$, the solution set of the inequality $f(x) \leqslant b$ is $\mathbb{R}$, find the range of the real number $b$.

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