
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
A shopping mall increases the purchase price of color TVs by 40% and then advertises a "big reward for customers, 20% off". As a result, each color TV makes a profit of 270 yuan. What is the purchase price of each color TV?  
Xiao Hong sets the purchase price of each color TV as x yuan and formulates the equation as: $x \times 40\% \times 80\% = x - 270$.  
Do you think her equation is correct? If it is correct, find the value of x; if it is not, formulate a new equation and find the value of x.

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