
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
(1) 5 students sign up for two extracurricular activity groups, with each student limited to signing up for one group. How many different registration methods are there in total?  
(2) There are banknotes of 0.1 yuan, 0.5 yuan, 1 yuan, 5 yuan, 10 yuan, 50 yuan, and 100 yuan, each one piece. How many different non-zero currency values can be formed in total?

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