
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
The number 531441 needs to be represented as the sum of several terms such that the first term is 1, the second term is $k$ times larger, the third term is $k$ times larger than the sum of the first two, the fourth term is $k$ times larger than the sum of all the previous terms, and so on. Find the multiplier $k$ and the number of terms, with the condition that the number of terms is no fewer than four.

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