
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 $g(n)$ represent the largest odd factor of natural number $n$. For example, $g(3)=3$ and $g(14)=7$. Find the value of $g(1) + g(2) + g(3) + \cdots + g\left(2^n\right)$.

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