
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 renovation program decided to demolish an old house and build a new one in its place. When dismantling the old house, two problems arose.

# 1
A pile of construction debris blocked access to certain points on the construction site, making it necessary to measure the distance between some points. The site manager measured the distance from point \( C \) to point \( A \) and from point \( C \) to point \( B \). It was found that \( \mathrm{AC}=4 \) meters and \( \mathrm{BC}=10 \) meters. Additionally, the distances \( \mathrm{CR}=1 \) meter, \( \mathrm{VR}=3 \) meters, and \( \mathrm{CV}=2.5 \) meters were determined for points \( R \) and \( V \), located on the extensions of the straight paths connecting objects A, C, and C, B respectively.

Determine the distance between points \( A \) and \( B \) (direct measurement on the site was not possible due to the debris) and the area of the section \( \mathrm{CADB} \), assuming the distances \( CD \) and \( \mathrm{BD} \) are twice the distance of \( CB \).

# 2
A rigid piece of rebar was sticking out of the ground, with a height of 0.5 meters above the ground. Attempts to pull it out of the ground were unsuccessful. The workers then moved it with a bulldozer such that the end of the rebar became level with the ground surface and was located 1.5 meters from its original entry point into the ground. Find the length of the part of the rebar hidden in the ground, assuming its lower end did not move.

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