
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
Explore how to design a planting plan based on the following information.

如何设计种植方案?

如何设计种植方案?

- Material $1$: Xiao Ming conducted extracurricular practice on his own 100 square meters of land with the theme of "planting crops". The relevant information of two crops, $A$ and $B$, is as shown in the table below:

  - Each square meter plants how many plants (plants): $2$ for crop $A$, $10$ for crop $B$.
  - Yield per plant (kg): $1.2$ for crop $A$, $0.5$ for crop $B$.

- Material $2$: Due to the large spacing between crop $A plants, the number of crop $A$ plants per square meter can be increased. After research, it was found that for every additional plant of crop $A$ per square meter, the yield per plant of crop $A$ decreases by $0.1$ kg.

- Material $3$: If both crop $A$ and crop $B$ are planted simultaneously, planting is done in separate areas.

问题解决

问题解决

- Single planting (all planting crop $A$):
  - Task $1$: Clarify the quantity relationship.
    - Let the number of additional crop $A$ plants per square meter be $x$ ($x$ is a positive integer), then there are ____ plants per square meter, and the yield per plant is ____ kg. (Expressed in algebraic expressions containing $x$).
  - Task $2$: Calculate the yield.
    - To make the yield of crop $A$ per square meter $4.8$ kg, how many plants should be planted per square meter?

- Planting in separate areas (planting crop $A$ and crop $B$):
  - Task $3$: Plan the planting plan.
    - Assume that $a$ square meters of the 100 square meters of land are used to plant crop $A, and the yield per square meter is maximized. The remaining area is planted with $10$ plants of crop $B$ per square meter. When the total yield of these 100 square meters is not less than $496$ kg, the range of values for $a$ is ____.

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