
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 a complex number $Z_1 = 2 + ai$ (where $a \in \mathbb{R}$ and $a>0$, $i$ is the imaginary unit), and $Z_1^2$ is a pure imaginary number.
(1) Find the value of the real number $a$.
(2) If $Z = \frac{Z_1}{1-i}$, find the modulus of the complex number $Z$.

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