
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 that the real numbers $a$, $b$, and $c$ satisfy $a \geq 1$, $b \geq 1$, $c \geq 1$, and $abc = 10$, and that $a^{\log_2{a}} \cdot b^{\log_2{b}} \cdot c^{\log_2{c}} \geq 10$, find the value of $a + b + c$.

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