
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 \( x \) and \( y \) are real numbers greater than 10, the leading digit of \( \lg x \) is \( a \) and the trailing digit is \( b \); the leading digit of \( \lg y \) is \( c \) and the trailing digit is \( d \). Additionally, it is known that \( |1 - a| + \sqrt{c - 4} = 1 \) and \( b + d = 1 \). Find the value of \( x \times y \).

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