
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 \(0 \leq x_{0} \leq \frac{\pi}{2}\) and \(x_{0}\) satisfies the equation \(\sqrt{\sin x + 1} - \sqrt{1 - \sin x} = \sin \frac{x}{2}\). If \(d = \tan x_{0}\), find the value of \(d\).

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