
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
Find the number of permutations  $( p_1, p_2, p_3 , p_4 , p_5 , p_6)$  of  $1, 2 ,3,4,5,6$  such that for any  $k, 1 \leq k \leq 5$ ,  $(p_1, \ldots, p_k)$  does not form a permutation of  $1 , 2, \ldots, k$ .

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