
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
First, convert the number 412$(_{5})$ into a decimal number, then use the "divide by k and take the remainder" method to convert it into a septimal (base 7) number.

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