
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
After investigating several households in a certain area, it was found that the annual income $x$ (in ten thousand yuan) and the annual food expenditure $y$ (in ten thousand yuan) have a linear relationship. The linear regression equation of $y$ with respect to $x$ is: $$\hat{y} = 0.254x + 0.321.$$ According to the regression equation, for every increase of 1 ten thousand yuan in annual income, the average increase in annual food expenditure is \_\_\_\_\_\_ ten thousand yuan.

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