
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
Given that $E=\{a_{1}, a_{2}, \ldots, a_{10}\}$, a subset $\{a_{k_{1}}, a_{k_{2}}, \ldots, a_{k_{n}}\}$ of $E$ is defined as the $k$-th subset of $E$, where $k=2^{k_{1}-1}+2^{k_{2}-1}+\ldots+2^{k_{n}-1}$. Then:  
(1) The subset $\{a_{1}, a_{3}\}$ is the $\_\_\_\_\_\_\_\_\_\_\_\_$-th subset of $E$;  
(2) The 211th subset of $E$ is $\_\_\_\_\_\_\_\_\_\_\_\_$.

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