
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
A natural number of five digits is called *Ecuadorian*if it satisfies the following conditions: $\bullet$  All its digits are different. $\bullet$  The digit on the far left is equal to the sum of the other four digits.  Example:  $91350$  is an Ecuadorian number since  $9 = 1 + 3 + 5 + 0$ , but  $54210$  is not since  $5 \ne 4 + 2 + 1 + 0$ .
Find how many Ecuadorian numbers exist.

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