
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
Let \\(z\\) be a complex number, \\(w=z+ \dfrac{1}{z} \\) be a real number, and \\(-1 < w < 2\\).

\\((1)\\) Find the value of \\(\left|z\right| \\) and the range of the real part of \\(z\\).

\\((2)\\) Let \\(\mu= \dfrac{1-z}{1+z} \\), find the minimum value of \\(w-\mu^{2} \\).

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