
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 $$f(x) = \begin{cases} 2a - \left(x + \frac{4}{x} \right), & x < a \\ x - \frac{4}{x}, & x \geq a \end{cases}.$$  
1. When $a=1$, if $f(x) = 3$, then find $x$.  
2. When $a \leq -1$, if $f(x) = 3$ has three distinct real roots that form an arithmetic sequence, then determine the value of $a$.

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