
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
For nonnegative integers  $n$ , let  $f(n)$  be the number of digits of  $n$  that are at least  $5$ . Let  $g(n)=3^{f(n)}$ . Compute
\[\sum_{i=1}^{1000} g(i).\]

[i]Proposed by Nathan Ramesh

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