
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 $f(x) = \begin{cases} 2a-x- \frac {4}{x}-3, & x\in (-\infty ,a) \\ x- \frac {4}{x}-3, & x\in [a,+\infty )\end{cases}$ has exactly 3 distinct zeros $x_1$, $x_2$, $x_3$ ($x_1 < x_2 < x_3$), and $2x_2 = x_1 + x_3$, find the value of $a$.

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