
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 $f(x)=-x^{3}+ax (a > 0)$.
(I) When $a=1$, find the equation of the tangent line that passes through the point $P(-1,0)$ and touches the curve $y=f(x)$;
(II) When $x \in [0,1]$, find the set of all possible values of $a$ such that the inequality $\frac{1}{4}x - \frac{1}{4} \leq f(x) \leq \frac{1}{4}x + \frac{1}{4}$ always holds.

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