
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
Integrate the following equations and find the particular solutions that satisfy the given initial conditions:
1) \((x+2) \, dy + (y-1) \, dx = 0, \, y(1) = 2\)
2) \(y' = (2y - 1) \, \cot(x), \, y\left(\frac{\pi}{6}\right) = 5\).

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