
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 $f(x)= \begin{cases} 2a-(x+ \frac {4}{x}),x < a\\x- \frac {4}{x},x\geqslant a\\end{cases}$.
(1) When $a=1$, if $f(x)=3$, then $x=$ \_\_\_\_\_\_;
(2) When $a\leqslant -1$, if $f(x)=3$ has three distinct real roots that form an arithmetic sequence, then $a=$ \_\_\_\_\_\_.

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