
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
Let \( x, y \in \mathbf{R} \). If \( 2x, 1, y-1 \) are in arithmetic sequence, and \( y+3 \), \( |x+1| + |x-1| \), \( \cos \left(\arcsin \sqrt{1-x^{2}}\right) \) are in geometric sequence, then \( (x+1)(y+1) = \) ______.

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