
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
Suppose a subset $\{a_{k_1},a_{k_2},\ldots,a_{k_n}\}$ of the set $E=\{a_1,a_2,\ldots,a_{10}\}$ is designated 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 $\boxed{\phantom{5}}$-th subset of $E$;  
(2) The 211-th subset of $E$ is $\boxed{\phantom{\{\}}}$.

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