
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 relations \( a_{1} = 1 \),

\[ a_{2n} = \begin{cases} 
a_{n}, & \text{if } n \text{ is even}, \\
2a_{n}, & \text{if } n \text{ is odd}
\end{cases} \]

and 

\[ a_{2n+1} = \begin{cases} 
2a_{n}+1, & \text{if } n \text{ is even}, \\
a_{n}, & \text{if } n \text{ is odd}
\end{cases}. \]

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

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