
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
Let  $n$  be a positive integer. Compute the number of words  $w$  that satisfy the following three properties.

1.  $w$  consists of  $n$  letters from the alphabet  $\{a,b,c,d\}.$ 2.  $w$  contains an even number of  $a$ 's

3.  $w$  contains an even number of  $b$ 's.

For example, for  $n=2$  there are  $6$  such words:  $aa, bb, cc, dd, cd, dc.$ 

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