
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 that \(x\) is an angle in the second quadrant, and \(\sin x + \cos x = a\) (where \(|a| \neq 1\)), find the values of the following expressions:
1. \(\operatorname{tg} x - \operatorname{ctg} x\)
2. \(\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 - \cos x}{1 + \cos x}}\)

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