
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
To protect the ecological environment, a mountainous area in our city has started to implement the policy of returning farmland to forest since 2005. It is known that at the end of 2004, the forest coverage area of this mountainous area was $a$ acres.  
(1) Assuming the annual natural growth rate of forest coverage area after returning farmland to forest is 2%, write the function relationship between the forest coverage area $y$ (in acres) and the number of years $x$ (in years) since the implementation of returning farmland to forest, and calculate the forest coverage area of this mountainous area at the end of 2009.  
(2) If by the end of 2014, the forest coverage area of this mountainous area needs to be at least twice that at the end of 2004, additional artificial greening projects must be implemented. What is the minimum annual average growth rate of the forest coverage area required to meet this goal by the end of 2014?  
(Reference data: $1.02^{4}=1.082$, $1.02^{5}=1.104$, $1.02^{6}=1.126$, $\lg2=0.301$, $\lg1.072=0.0301$)

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