
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 $f(x)= \begin{cases} 2-x,x > 0 \\ x+2,x < 0 \end{cases}$, and $F(x)=xf(x)$

1. If $F(a)=3$, find the value of $a$;
2. If $F(x) < 0$, find the set of all possible values of $x$.

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