
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 real function \( f \) has the property that, whenever \( a \), \( b \), \( n \) are positive integers such that \( a \times b = 2^n \), the equation
\[ f(a) + f(b) = n^2 \]
holds. Determine \( f(2048) \).

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