
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
Count the number of permutations \( a_{1} a_{2} \ldots a_{7} \) of 1234567 with the longest decreasing subsequence of length at most two (i.e. there does not exist \( i < j < k \) such that \( a_{i} > a_{j} > a_{k} \)).

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