
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
A sequence $\left\{a_{n}\right\}$ is defined as follows: $a_{1}=1$, and for $n \geqslant 2$,
$$
a_{n}=\left\{\begin{array}{l}
\frac{a_{n-1}}{2}+1, \text { when } n \text { is even;} \\
\frac{1}{a_{n-1}}, \text { when } n \text { is odd.}
\end{array}\right.
$$

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