
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
Given a three-digit number with digits $x, y, z$, where $x$ is the first digit, $z$ is the third digit, and $y$ is the second digit, the number is not divisible by $5$, has digits that sum to less than $15$, and $x=z>y$, calculate the number of such numbers.

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