
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
Given two distinct geometric progressions with first terms both equal to 1, and the sum of their common ratios equal to 3, find the sum of the fifth terms of these progressions if the sum of the sixth terms is 573. If the answer is ambiguous, provide the sum of all possible values of the required quantity.

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