
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
Let \( f(n) \) be the number of ways to write \( n \) as a sum of powers of 2, where the order of the summation is considered. For example, \( f(4) = 6 \) because 4 can be written as \( 4 \), \( 2 + 2 \), \( 2 + 1 + 1 \), \( 1 + 2 + 1 \), \( 1 + 1 + 2 \), and \( 1 + 1 + 1 + 1 \). Find the smallest \( n \) greater than 2013 for which \( f(n) \) is odd.

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