
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 non-zero vector sequence $\{\overrightarrow{a_n}\}$ that satisfies $\overrightarrow{a_1} = (1, 1)$ and $\overrightarrow{a_n} = (x_n, y_n) = \frac{1}{2}(x_{n-1} - y_{n-1}, x_{n-1} + y_{n-1})$ (for $n \geq 2$ and $n \in \mathbb{N}^*$), consider the following statements:  
1. The sequence $\{|\overrightarrow{a_n}|\}$ is an arithmetic sequence;  
2. $|\overrightarrow{a_1}| \cdot |\overrightarrow{a_5}|= \frac{1}{2}$;  
3. Let $c_n = 2\log_2|\overrightarrow{a_n}|$, then the sum of the first $n$ terms of the sequence $\{c_n\}$ is $T_n$, and $T_n$ achieves its maximum value if and only if $n=2$;  
4. Denote the angle between $\overrightarrow{a_n}$ and $\overrightarrow{a_{n-1}}$ as $\theta_n$ (for $n \geq 2$), and it is always true that $\theta_{n} = \frac{\pi}{4}$. Identify all correct statements from the list.

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