
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
If $a$, $b$, and $c$ are the three sides of a triangle, and the perimeter of the triangle is $18$ cm, and $a + b = 2c$, $b = 2a$; then $a =$ ____ $cm$, $b =$ ____ $cm$, $c =$ ____ $cm$.

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