
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 "Christmas tree" of height 1 is inscribed in the graph of a function that is symmetric with respect to the y-axis. It is known that the "branches" of the tree form an angle of $45^\circ$ with the vertical. Find the perimeter of the tree (i.e., the sum of the lengths of all the green segments).

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