
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 permutation  $\sigma$  of the numbers  $1,2,\ldots , 10$  is called  $\textit{bad}$  if there exist integers  $i, j, k$  which satisfy
\[1 \leq i < j < k \leq 10 \quad \text{ and }\quad \sigma(j) < \sigma(k) < \sigma(i)\]
and  $\textit{good}$  otherwise. Find the number of  $\textit{good}$  permutations.

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