
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 particle moves in the Cartesian plane from point $(0,0)$ to $(3,3)$ following these rules:
- From any point $(a,b)$, the particle can move to $(a+1,b), (a,b+1), (a+1,b+1),$ or $(a-1, b+1)$.
- The particle may not take more than 2 diagonal steps in its entire journey.
- There are no right-angle turns in the particle's path.
How many different paths can the particle take from $(0,0)$ to $(3,3)$?

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