
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 desired 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 allowed daily feed consumption of $8 \mathrm{~kg}$.

(a) Represent the conditions of the problem algebraically.

(b) Represent the conditions of the problem graphically in the Cartesian plane $xOy$.

(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 desired spaces and the maximum feed consumption? And for chicks?

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