
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
Find the pattern and fill in the blanks.
$$
\begin{array}{l}
3, 7, 15, 31, 63, \ldots, \\
1, 9, 3, 10, 5, \ldots, 12, 9 .
\end{array}
$$

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