
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
Quantities \( a \) and \( b \) vary inversely. When \( a \) is \( 800, \) \( b \) is \( 0.5. \) What is the value of \( b \) when \( a \) is \( 1600 \)? Express your answer as a decimal to the nearest thousandths.

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