
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 chicken coop with an area of $240 \mathrm{~m}^{2}$ should house chickens and chicks, with a desirable free space of $4 \mathrm{~m}^{2}$ for each chicken and $2 \mathrm{~m}^{2}$ for each chick. Additionally, each chick eats $40 \mathrm{~g}$ of feed per day and each chicken eats $160 \mathrm{~g}$ per day, with a maximum daily feed allowance of $8 \mathrm{~kg}$. 

(a) Represent algebraically the problem conditions.

(b) Graphically represent the above conditions on the Cartesian plane $x O y$.

(c) Can this chicken coop accommodate 20 chickens and 80 chicks? And 30 chickens and 100 chicks?

(d) What is the maximum number of chickens that can be placed in the coop, respecting the desirable spaces and the maximum feed allowance? And of chicks?

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