
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
The digits $1, 2, 3, 4, 5,$ and $6$ can be arranged to form various $6$-digit positive integers with six distinct digits. How many such integers have the digit $1$ to the left of the digit $2$ and the digit $3$ to the left of the digit $4$? (The digits $1$ and $2$ and $3$ and $4$ do not have to be adjacent to each other.)

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