
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
Suppose \( a \), \( b \), and \( c \) are such that \( a \) and \( b \) are inversely proportional, and likewise \( b \) and \( c \) are inversely proportional. If \( a = 40 \) when \( b = 5 \), and \( c = 10 \) when \( b = 7 \), find the value of \( c \) when \( a = 16 \).

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