
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
Consider two sequences: The first consists of all positive integers which are powers of 3 or sums of distinct powers of 3, and the second consists of all positive integers which are powers of 5 or sums of distinct powers of 5. Find the smallest number that appears in both sequences and is at least the 150th term in the sequence of powers of 3.

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