
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
An increasing sequence \(1, 3, 4, 9, 10, 12, 13, \cdots\) is formed by some positive integers, which are either powers of 3, or sums of different powers of 3. Find the 100th term of this sequence.

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