
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 increasing sequence  $1,3,4,9,10,12,13\cdots$  consists of all those positive integers which are powers of 3 or sums of distinct powers of 3. Find the  $100^{\text{th}}$  term of this sequence.

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