
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  $1; 3; 4; 9; 10; 12; 13; 27; 28; 30; 31, \ldots$  is formed with positive integers which are powers of  $3$  or sums of different powers of  $3$ . Which number is in the  $100^{th}$  position?

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