
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 a set $M=\{a_1, a_2, \ldots, a_n\}$ ($n \in \mathbb{N}^*$), its subset $\{a_{i_1}, a_{i_2}, \ldots, a_{i_m}\}$ ($m \in \mathbb{N}^*$) is defined as the $k$-th subset of $M$, where $k=2^{i_1-1}+2^{i_2-1}+\ldots+2^{i_n-1}$. Then, the 25th subset of $M$ is \_\_\_\_\_\_.

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