
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 $f(x) = (x - t)|x| (t \in \mathbb{R})$.

1. Discuss the monotonic intervals of the function $f(x)$.
2. If $\exists t \in (0, 2)$, for $\forall x \in [-1, 2]$, the inequality $f(x) > x + a$ always holds, find the range of the real number $a$.

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