
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 ladder is $2 \frac{2}{3}$ meters shorter than the height of the wall. If we lean it against the wall such that the foot of the ladder is at a distance from the wall equal to $\frac{3}{5}$ of the ladder's length, then the top of the ladder reaches $\frac{2}{5}$ of the height of the wall. How long is the ladder?

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