
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
Euclid Paracelsus Bombast Umbudjo is trying to supplement his meager professor's salary by participating in prize competitions organized by a soap company. In one of these contests, participants are asked to determine the number of paths on a given diagram that spell out the word "MATHEMATICIAN." Umbudjo counted 1587 paths starting in one of the first five rows. When the time came to report the results, he was quite puzzled, to say the least. Help the professor count all the paths using as few calculations as possible.
```
M
                                    M A M
M A T A M
M A T H T A M
M A T H E H T A M
M A T H E M E H T A M
M A T H E M A M E H T A M
M A T H E M A T A M E H T A M
M A T H E M A T I T A M E H T A M
M A T H E M A T I C I T A M E H T A M
M A T H E M A T I C I C I T A M E H T T A M
M A T H E M A T I C I A I C I T A M E H T A M
M A T H E M A T I C I A N A I C I T A M E E H T A A M
```

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