
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
In $f(m, n)$, where $m, n, f(m, n) \in \mathbb{N}^*$, and for any $m, n$, the following conditions hold: (1) $f(1, 1) = 1$; (2) $f(m, n+1) = f(m, n) + 2$; (3) $f(m+1, 1) = 2f(m, 1)$. Given the following three statements: ① $f(1, 5) = 9$; ② $f(5, 1) = 16$; ③ $f(5, 6) = 26$. The number of correct statements is ___.

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