
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 an arithmetic sequence $\{a_n\}$ with the general term formula $a_n = 2n - 1$, insert one 2 between $a_1$ and $a_2$, two 2's between $a_2$ and $a_3$, and so on, inserting $n$ 2's between $a_n$ and $a_{n+1}$ to form a new sequence $\{b_n\}$. If $a_{10} = b_k$, find the value of $k$.

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