
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
At the Smartpup Tricks Academy, there are groups of dogs trained in three skills: fetch, jump, and play dead. The number of dogs trained in each skill and combination are:
\begin{tabular}{l@{\qquad}l}
40 dogs can fetch & 14 dogs can fetch and jump \\
35 dogs can jump & 10 dogs can jump and play dead \\
22 dogs can play dead & 16 dogs can fetch and play dead \\
6 dogs can do all three & 12 dogs can do none
\end{tabular}

How many dogs are in total at the academy?

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