
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 according to the following rules: 

1.  From any lattice point  $ (a,b)$ , the particle may only move to  $ (a \plus{} 1,b)$ ,  $ (a,b \plus{} 1)$ , or  $ (a \plus{} 1,b \plus{} 1)$ .
2. There are no right angle turns in the particle's path. 

How many different paths can the particle take from  $ (0,0)$  to  $ (5,5)$ ?

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