
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 frog is placed at the [origin](https://artofproblemsolving.com/wiki/index.php/Origin) on the [number line](https://artofproblemsolving.com/wiki/index.php/Number_line), and moves according to the following rule: in a given move, the frog advances to either the closest [point](https://artofproblemsolving.com/wiki/index.php/Point) with a greater [integer](https://artofproblemsolving.com/wiki/index.php/Integer) [coordinate](https://artofproblemsolving.com/wiki/index.php/Coordinate) that is a multiple of 3, or to the closest point with a greater integer coordinate that is a multiple of 13. A move sequence is a [sequence](https://artofproblemsolving.com/wiki/index.php/Sequence) of coordinates that correspond to valid moves, beginning with 0 and ending with 39. For example, $0,\ 3,\ 6,\ 13,\ 15,\ 26,\ 39$ is a move sequence. How many move sequences are possible for the frog?

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