
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
Factorize the following expressions:

1) \(x^{4} - 8x^{2} + 4\)  
2) \(4a^{4} - 12a^{2} + 1\)  
3) \(b^{5} + b + 1\)  
4) \(ab(a - b) - ac(a + c) + cb(2a + c - b)\)

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