
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
Arrange the digits 1, 2, 3, 4, 5, 6 in a sequence where the i-th number is $a_i$ (for $i=1,2, \ldots, 6$). If $a_1 \neq 1$, $a_3 \neq 3$, $a_5 \neq 5$, and $a_1 < a_3 < a_5$, how many different permutations are there?

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