
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 company plans to build a glass partition wall in their office lobby with a length of $a$ meters. They will first install $x$ pillars at equal distances, then install a piece of glass with the same height and specifications as the pillars between each adjacent pair of pillars. The cost of one pillar is 6400 yuan, and the cost of a glass panel with a length of $m$ meters is $(50m + 100m^2)$ yuan. Assume that the thickness of all pillars is negligible and disregard other factors. Let $y$ represent the total cost in yuan (total cost = pillar cost + glass cost).

1. Find the function relationship between $y$ and $x$.
2. When $a = 56$, how should the design be optimized to minimize the total cost?

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