
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

The sequence is defined by the recurrence relations \( a_{1} = 1 \),

\[ 
a_{2n} = \left\{
\begin{array}{ll}
a_{n}, & \text{if } n \text{ is even,} \\
2a_{n}, & \text{if } n \text{ is odd;}
\end{array}
\right. \quad
a_{2n+1} = \left\{
\begin{array}{ll}
2a_{n}+1, & \text{if } n \text{ is even,} \\
a_{n}, & \text{if } n \text{ is odd.}
\end{array}
\right.
\]

Find the smallest natural number \( n \) for which \( a_{n} = a_{2017} \).

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