
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
Consider the integer \( n \geqslant 2 \), and the set 
\[
A_{n}=\{2^{n}-2^{k} \mid k \in \mathbf{Z}, 0 \leqslant k < n\}.
\]
Find the largest positive integer that cannot be expressed as a sum of one or more (repetitions allowed) elements from the set \( A_{n} \).

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