
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 $x, y \in \{x | x = a + a_1 \cdot 10 + a_2 \cdot 100\}$, where $a_i \in \{1, 2, 3, 4, 5, 6, 7\}$ ($i=0, 1, 2$), and $x+y=636$. Calculate the number of distinct points $(x, y)$ on the coordinate plane.

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