
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
Calculate the value of the function:

1) \( f(x) = \sqrt{x^2 - 5x + 4} \)

   a) when \( x = 0 \); b) when \( x = a + 1 \);

2) \( \varphi(x) = 2 \arcsin x + \operatorname{arctg} 2x \) when \( x = -\frac{1}{2} \);

3) \( y = x^2 \arccos \frac{x}{2} - 3x \operatorname{arcctg} x \) when \( x = -1 \).

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