
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
$BC, CA, AB$ are divided respectively by the points $X, Y, Z$ in the ratio $1:2$. Let
area of $\triangle AZY$ : area of $\triangle ABC = 2: a$ and
area of $\triangle AZY$ : area of $\triangle XYZ = 2: b$.

1. Find the value of $a$.
2. Find the value of $b$.

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