
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 there be three groups of real numbers: \(a_{1} < a_{2} < \cdots < a_{n_{n}}\); \(b_{1} < b_{2} < \cdots < b_{n_{2}}\); \(c_{1} < c_{2} < \cdots < c_{n_{3}}\). If we interleave these numbers to form a single sequence while maintaining the increasing order within each group, determine the number of different sequences that can be formed.

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