
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
Elective 4-5: Special Topics on Inequalities

Let $f(x)=|x-1|-|x+3|$.

(1) Solve the inequality $f(x) > 2$;

(2) If the inequality $f(x) \leqslant kx + 1$ holds for all $x \in [-3,-1]$, find the range of the real number $k$.

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