
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
A sequence is defined by the following conditions: the first term is 3, the second term is 6, the third term is 18, and each subsequent term is twice the sum of all previous terms. What is the sixth term? From which term in this sequence does every term begin to exceed 2007?

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