
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 $n^*$ signifies $\frac{1}{n}$. Determine how many of the following statements are true:

i) $4^* + 8^* = 12^*$
ii) $10^* - 5^* = 7^*$
iii) $3^* \cdot 9^* = 27^*$
iv) $15^* + 5^* = 10^* + 10^*$
A) 0 
B) 1 
C) 2 
D) 3 
E) 4

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