
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
Find, as a function of  $\, n, \,$  the sum of the digits of 
\[ 9 \times 99 \times 9999 \times \cdots \times \left( 10^{2^n} - 1 \right),  \] 
where each factor has twice as many digits as the previous one.

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