
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 the vectors \( \bar{a}\{3 ;-4 ; 5\} \) and \( \bar{b}\{-1 ; 0 ;-2\} \), find the coordinates of the vector \( \bar{c}=2 \bar{a}+5 \bar{b} \).

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