
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 via a sequence of steps, each of length one.  Each step is left, right, up, or down, all four equally likely.  Let  $p$  be the probability that the object reaches  $(2,2)$  in six or fewer steps.  Given that  $p$  can be written in the form  $m/n,$  where  $m$  and  $n$  are relatively prime positive integers, find  $m+n.$ 

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