
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
Starting at $(0,0),$ an object moves in the coordinate plane using steps each of length one in either left, right, up, or down directions, with all directions equally probable. Let \( q \) be the probability that the object reaches $(3,3)$ in either six or eight steps. Given that \( q \) can be expressed as \( \frac{a}{b} \), where \( a \) and \( b \) are co-prime positive integers, determine \( a+b \).

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