
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
Find the derivatives of the following functions:
1) \( y = 5 \arcsin(kx) + 3 \arccos(kx) \)
2) \( y = \arcsin\left(\frac{a}{x}\right) - \operatorname{arcctg}\left(\frac{x}{a}\right) \)
3) \( r = \operatorname{arctg}\left(\frac{m}{\varphi}\right) + \operatorname{arcctg}(m \operatorname{ctg}(\varphi)) \)
   - \( r'(0) \) ?
   - \( r'(\pi) \) ?

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