
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
Given a triangle \( \triangle ABC \) with \( \angle ABC = 80^\circ \), \( \angle ACB = 70^\circ \), and \( BC = 2 \). A perpendicular line is drawn from \( A \) to \( BC \), and another perpendicular line is drawn from \( B \) to \( AC \). The two perpendicular lines intersect at \( H \). Find the length of \( AH \).

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