
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  $P_1,P_2,\dots,P_{720}$  denote the integers whose digits are a permutation of  $123456$ , arranged in ascending order (so  $P_1=123456$ ,  $P_2=123465$ , and  $P_{720}=654321$ ). What is  $P_{144}$ ?

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