
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
Consider the function $y=H(x)$ defined as $H(x) = (x-3)^2/2 - 2$. A portion of the graph is shown below, where the distance between grid lines is $1$ unit.

Compute $H(H(H(H(H(2)))))$.

[graph description not visually displayed]
Suppose through the graph you know that:
- $H(2) = 1/2$
- $H(1/2) = 5$
- $H(5) = 1/2$

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