
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 that $a \in \mathbb{R}$, let the function $f(x) = x|x - a| - x$.
(I) When $a = 1$, find the monotonic intervals of the function $f(x)$;
(II) If $a \leqslant 1$, for any $x \in [0, t]$, the inequality $-1 \leqslant f(x) \leqslant 6$ always holds. Find the maximum value of the real number $t$ and the value of $a$ at this time.

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