
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
You have a set of four weights measuring 1 lb, 3 lb, 9 lb, and 27 lb. What is the heaviest single object you can accurately weigh with these weights, and how many different objects (in terms of weight) can you weigh using any combination of these weights?
A) 12
B) 13 
C) 40
D) 29

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