
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
The function \( f(x) \) satisfies the condition: for any real numbers \( a \) and \( b \), the equality \( f\left(\frac{a+2b}{3}\right) = \frac{f(a)+2f(b)}{3} \) holds. Find the value of the function \( f(2022) \), if \( f(1) = 1 \), \( f(4) = 7 \).

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